Trigonometric functions

This page describes the available functions to assist with performing trigonometric calculations.

tip

Positive and negative infinity values are expressed as 'Infinity' or '-Infinity' in QuestDB.

sin#

sin(angleRadians) returns the trigonometric sine of an angle.

Arguments#

angleRadians is a numeric value indicating the angle in radians.

Return value#

Return value type is double.

Description#

Special case: if the argument is NaN or an infinity, then the result is Null.

Examples#

SELECT pi()/2 angle, sin(pi()/2) sin;

angle	sin
1.570796326794	1

cos#

cos(angleRadians) returns the trigonometric cosine of an angle.

Arguments#

angleRadians numeric value for the angle, in radians.

Return value#

Return value type is double.

Description#

Special case: if the argument is NaN or an infinity, then the result is Null.

Examples#

SELECT pi()/2 angle, cos(pi()/2) cos;

angle	cos
1.570796326794	6.123233995736766e-17

tan#

tan(angleRadians) returns the trigonometric tangent of an angle.

Arguments#

angleRadians numeric value for the angle, in radians.

Return value#

Return value type is double.

Description#

Special case: if the argument is NaN or an infinity, then the result is Null.

Examples#

SELECT pi()/2 angle, tan(pi()/2) tan;

angle	tan
1.570796326794	16331239353195370

cot#

cot(angleRadians) returns the trigonometric cotangent of an angle.

Arguments#

angleRadians numeric value for the angle, in radians.

Return value#

Return value type is double.

Description#

Special case: if the argument is NaN, 0, or an infinity, then the result is Null.

Examples#

SELECT pi()/2 angle, cot(pi()/2) cot;

angle	cot
1.570796326794	6.123233995736766e-17

asin#

asin(value) the arcsine of a value.

Arguments#

value is a numeric value whose arcsine is to be returned.

Return value#

Return value type is double. The returned angle is between -pi/2 and pi/2 inclusively.

Description#

Special case: if the argument is NaN or an infinity, then the result is Null.

Examples#

SELECT asin(1.0) asin;

asin
1.570796326794

acos#

acos(value) returns the arccosine of a value.

Arguments#

value is a numeric value whose arccosine is to be returned. The returned angle is between 0.0 and pi inclusively.

Return value#

Return value type is double.

Description#

Special cases: if the argument is NaN or its absolute value is greater than 1, then the result is Null.

Examples#

SELECT acos(0.0) acos;

acos
1.570796326794

atan#

atan(value) returns the arctangent of a value.

Arguments#

value is a numeric value whose arctangent is to be returned.

Return value#

Return value type is double. The returned angle is between -pi/2 and pi/2 inclusively.

Description#

Special cases:

If the argument is NaN, then the result is Null.
If the argument is infinity, then the result is the closest value to pi/2 with the same sign as the input.

Examples#

Special case where input is '-Infinity':

SELECT atan('-Infinity');

Returns the closest value to pi/2 with the same sign as the input:

atan
-1.570796326794

SELECT atan(1.0) atan;

atan
0.785398163397

atan2#

atan2(valueY, valueX) returns the angle theta from the conversion of rectangular coordinates (x, y) to polar (r, theta). This function computes theta (the phase) by computing an arctangent of y/x in the range of -pi to pi inclusively.

Arguments#

valueY numeric ordinate coordinate.
valueX numeric abscissa coordinate.

note

The arguments to this function pass the y-coordinate first and the x-coordinate second.

Return value#

Return value type is double between -pi and pi inclusively.

Description:#

atan2(valueY, valueX) measures the counterclockwise angle theta, in radians, between the positive x-axis and the point (x, y):

Atan2 trigonometric function

Special cases:

input `valueY`	input `valueX`	`atan2` return value
0	Positive value	0
Positive finite value	'Infinity'	0
-0	Positive value	0
Negative finite value	'Infinity'	0
0	Negative value	Double value closest to pi
Positive finite value	'-Infinity'	Double value closest to pi
-0	Negative value	Double value closest to -pi
Negative finite value	'-Infinity'	Double value closest to -pi
Positive value	0 or -0	Double value closest to pi/2
'Infinity'	Finite value	Double value closest to pi/2
Negative value	0 or -0	Double value closest to -pi/2
'-Infinity'	Finite value	Double value closest to -pi/2
'Infinity'	'Infinity'	Double value closest to pi/4
'Infinity'	'-Infinity'	Double value closest to 3/4 * pi
'-Infinity'	'Infinity'	Double value closest to -pi/4
'-Infinity'	'-Infinity'	Double value closest to -3/4 * pi

Examples#

SELECT atan2(1.0, 1.0) atan2;

atan2
0.785398163397

radians#

radians(angleDegrees) converts an angle measured in degrees to the equivalent angle measured in radians.

Arguments#

angleDegrees numeric value for the angle in degrees.

Return value#

Return value type is double.

Examples#

SELECT radians(180);

radians
3.141592653589

degrees#

degrees(angleRadians) converts an angle measured in radians to the equivalent angle measured in degrees.

Arguments#

angleRadians numeric value for the angle in radians.

Return value#

Return value type is double.

Examples#

SELECT degrees(pi());

degrees
180

pi#

pi() returns the constant pi as a double.

Arguments#

None.

Return value#

Return value type is double.

Examples#

SELECT pi();

pi
3.141592653589